Portfolio Average Return Calculation Explained

This question requires us to calculate the average return of a stock portfolio composed of three distinct stocks. Each stock has a specific weight within the portfolio and a corresponding individual return. The average return of the portfolio is essentially a weighted average of the individual stock returns, where the weights are the proportions of the portfolio each stock constitutes.

Portfolio Components and Their Returns

We are given the following details for each stock in the portfolio:

• Stock A: Constitutes 30% of the portfolio and yields a 5% return.
• Stock B: Constitutes 40% of the portfolio and yields a 10% return.
• Stock C: Constitutes the remaining 30% of the portfolio and yields an 8% return.

Let's verify the total weight: $30\% + 40\% + 30\% = 100\%$. This confirms the portfolio is fully allocated.

Calculating the Weighted Average Return

The formula to calculate the weighted average return ($R_p$) for a portfolio is:

$$ R_p = \sum_{i=1}^{n} (w_i \times R_i) $$

In this case, with three stocks (A, B, and C), the formula becomes:

$$ R_p = (w_A \times R_A) + (w_B \times R_B) + (w_C \times R_C) $$

Where:

• $w_A, w_B, w_C$ are the portfolio weights (as decimals) for Stock A, Stock B, and Stock C.
• $R_A, R_B, R_C$ are the individual returns (as decimals) for Stock A, Stock B, and Stock C.

First, we need to convert the given percentages into decimal form for calculation:

• Weight of Stock A ($w_A$): $30\% = 0.30$
• Weight of Stock B ($w_B$): $40\% = 0.40$
• Weight of Stock C ($w_C$): $30\% = 0.30$
• Return of Stock A ($R_A$): $5\% = 0.05$
• Return of Stock B ($R_B$): $10\% = 0.10$
• Return of Stock C ($R_C$): $8\% = 0.08$

Now, plug these decimal values into the weighted average formula:

$$ R_p = (0.30 \times 0.05) + (0.40 \times 0.10) + (0.30 \times 0.08) $$

Calculate the contribution of each stock to the total portfolio return:

• Stock A's contribution: $0.30 \times 0.05 = 0.015$
• Stock B's contribution: $0.40 \times 0.10 = 0.040$
• Stock C's contribution: $0.30 \times 0.08 = 0.024$

Sum these contributions to find the portfolio's average return in decimal form:

$$ R_p = 0.015 + 0.040 + 0.024 $$

$$ R_p = 0.079 $$

Portfolio Average Return Result

To express the final average portfolio return as a percentage, we multiply the decimal result by 100:

$$ \text{Average Portfolio Return} = 0.079 \times 100\% = 7.9\% $$

Thus, the average return of the stock portfolio is 7.9%.